Skip to main content
SpringerLink
Log in

Monod's bacterial growth model revisited

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

An attempt to justify Monod's bacterial growth model is presented. The justification is based on a mechanistic approach to growth which leads to a differential equation with delay and then to Monod's model. An unexpected increase of parameterK s with μm is predicted by the theory. A survey of literature shows that this effect is present in a large majority of published data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Billen, G. 1984. Heterotrophic utilization and regeneration of nitrogen InHeterotrophic Activity in the Sea, J. E. Hobbie and P. J. L. Williams (eds), pp. 313–355. New York, Plenum Press.

    Google Scholar 

  • Billen, G. and P. Servais, 1989. Modélistion des processus de dégradation bactérienne de la matière organique en milieu aquatique. InMicro-organimes dans les Écosystèmes Océaniques, M. Bianchi, D. Marty, P. Caumette, J. C. Bertrand and M. Gauthier (eds), pp. 219–245. Paris: Masson.

    Google Scholar 

  • Briggs, G. E. and J. B. S. Haldane. 1925. A note on the kinetics of enzyme action.Biochem. J. 19, 338–339.

    Google Scholar 

  • Caperon, J. 1967. Population growth in micro-organisms limited by food supply.Ecology 48, 715–722.

    Article  Google Scholar 

  • Comby, S., J. P. Flandrois, G. Carret and C. Pichat. 1988. Mathematical modelling of bacterial growth at subinhibitory levels of aminoglycosides.Annls Inst. Pasteur/Microbiol. 139, 613–629.

    Google Scholar 

  • Corman, A., G. Carret, A. Pavé, J. P. Flandrois and C. Couix. 1986. Bacterial growth measurement using an automated system: mathematical modelling and analysis of growth kinetics.Annls Inst. Pasteur/Microbiol. 137B, 133–143.

    Google Scholar 

  • Endo, K. and T. Mochizuki. 1979. Relation between specific growth rate of rotifer.Brachionus plicatilis, and concentration of food, marine species ofChlorella.J. Ferment. Technol. 57, 372–374.

    Google Scholar 

  • Gibson, A. M., N. Bratchell and T. A. Roberts. 1987. The effect of sodium chloride and temperature on the rate and extent of growth ofClostridium botulinum type A in pasteurized pork slurry.J. appl. Bacteriol. 62, 479–490.

    Google Scholar 

  • Gompertz, B. 1825. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies.Phil. Trans. R. Soc. Lond. 115, 513–585.

    Google Scholar 

  • Gould, I. M., A. C. Jason and K. Milne. 1989. Use of the Malthus microbial growth analyser to study the post antibiotic effect of antibiotics.J. Antimicrob. Chemother. 24, 523–531.

    Google Scholar 

  • Harris, C. M. and D. B. Kell. 1985. The estimation of microbial biomass.Biosensors 1, 17–84.

    Article  Google Scholar 

  • Healey, F. P. 1980. Slope of the Monod equation as an indicator of advantage in nutrient competition.Microb. Ecol. 5, 281–286.

    Article  Google Scholar 

  • Itoh, S. and K. Takahashi. 1984. Calorimetric studies of microbial growth: kinetic analysis of growth thermograms observed for Bakery Yeast at various temperature.Agric. Biol. Chem. 48, 271–275.

    Google Scholar 

  • Jason, A. C. 1983. A deterministic model for monophasic growth of batch cultures of bacteria.Antonie van Leeuwenhoek 49, 513–536.

    Article  Google Scholar 

  • Jones, R. C. and J. S. Hough. 1970 The effect of temperature on the metabolism of Baker's Yeast growing on continuous culture.J. gen. Microbiol. 60, 107–116.

    Google Scholar 

  • Knowles, G., A. L. Downing and M. J. Barrett. 1965. Determination of kinetic constants for nitrifying bacteria in mixed culture, with the aid of an electronic computer.J. gen Microbiol. 38, 263–278.

    Google Scholar 

  • MacDonald, N. 1978. Time lags in biological models.Lect. Notes Biomath. 27, 1–112.

    Google Scholar 

  • Mechling, J. A. and S. S. Kilham. 1982. Temperature effects on silicon limited growth of the lake Michigan diatomStephanodiscus minutus (Bacillariophyceae).J. Phycol. 18, 199–205.

    Article  Google Scholar 

  • Michaelis, L. and M. L. Menten. 1913. Die Kinetic der Iinvertinwirkung.Biochem Z. 49, 334–369.

    Google Scholar 

  • Mitsuhashi, S. and S. Takeuchi. 1951. On the bacterial growth by shaking culture method.Jap. J. exp. Med. 21, 1–5.

    Google Scholar 

  • Monod. J. 1941.Recherches sur la croissance des cultures bactériennes Thèse de docteur ès sciences naturelles, Paris.

  • Monod, J. 1949. The growth of bacterial cultures.A. Rev. Microbiol. 3, 371–394.

    Article  Google Scholar 

  • Monod, J. 1950. La technique de culture continue: théorie et applications.Annls Inst. Pasteur 79, 390–410.

    Google Scholar 

  • Morrison, K. A., N. Thérien and B. Marcos. 1987. Comparison of six models for nutrient limitations on phytoplankton growth.Can. J. Fish. aquat. Sci. 44, 1278–1288.

    Google Scholar 

  • Muck, R. E. and C. P. L. Grady. 1974. Temperature effects on microbial growth in CSTR's.J. environ. Engng Div. 100, 1147–1163.

    Google Scholar 

  • Neidhardt, F. C., J. L. Ingraham, K. B. Low, B. Magasanik, M. Schaechter and H. E. Umbarger (eds). 1987. Escherichia coliand Salmonella typhimurium.cellular and molecular biology, Vol. 1, pp. 127–806. Washington: Libary of Congress.

    Google Scholar 

  • Pearl, R. and L. J. Reed. 1920. On the rate of growth of the population of the United States since 1790 and its mathematical representation.Proc. natn. Acad. Sci. U.S.A. 6, 275–288.

    Article  Google Scholar 

  • Richards, O. W. 1928. The growth of the yeastSaccharomyces cerevisiae I. The growth curve, its mathematical analysis, and the effect of temperature on the yeast growth.Annls Bot. 42, 271–283.

    Google Scholar 

  • Richards, F. J. 1959. A flexible growth function for empirical use.J. exp. Bot. 10, 290–300.

    Google Scholar 

  • Rochet, M. J. and J. P. Flandrois. 1989. Bacterial strain characterization using mathematical modelling of growth.Zbl. Bakt. 271, 2–10.

    Google Scholar 

  • Senft, W. H., R. A. Hunchberger and K. E. Roberts. 1981. Temperature dependance of growth and phosphorus uptake in two species ofVolvox (Volvocales, Chlorophyta).J. Physicol. 17, 323–329.

    Article  Google Scholar 

  • Shelef, G., W. J. Oswald and C. C. Golueke. 1970. Assaying algal growth with respect to nitrate concentration by a continuous flow turbidostat.Proc. Int. Conf. Water Pollut. Res. 3, 1–9.

    Google Scholar 

  • Simkins, S., R. Mukherjee and M. Alexander. 1986. Two approaches to modeling kinetics of biodegradation by growing cells and application of a two-compartment model for mineralization kinetics in sewage.Appl. environ. Microbiol. 51, 1153–1160.

    Google Scholar 

  • Tilman, D., S. S. Kilham and P. Kilham. 1982. Phytoplankton community ecology: the role of limiting nutrients.Ann. Rev. ecol. Syst. 13, 349–372.

    Article  Google Scholar 

  • Topiwala, H. and C. G. Sinclair. 1971. Temperature relationship in continuous culture.Biotech. Bioeng. 13, 795–813.

    Article  Google Scholar 

  • Verhulst, P. F. 1845. Recherches mathématiques sur la loi d'accroissement de la population.Mém. Acad. r. Sci. Lett. Belg. 18, 1–38.

    Google Scholar 

  • Verhulst, P. F. 1847. Deuxième mémoire sur la loi d'accroissement de la population.Mém. Acad. r. Sci. Lett. Belg. 20, 1–32.

    Google Scholar 

  • Zwietering, M. H., I. Jongenburger, F. M. Rombouts and K. Van't Riet. 1990. Modeling of the bacterial growth curve.Appl. environ. Microbiol. 56, 1875–1881.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS URA 243, Laboratoire de Biométrie, Université Claude Bernard, 43 Boulevard du 11 Novembre, 69622, Villeurbanne, France

    J. R. Lobry, J. P. Flandrois, G. Carret & A. Pave

Authors
  1. J. R. Lobry
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. P. Flandrois
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Carret
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Pave
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lobry, J.R., Flandrois, J.P., Carret, G. et al. Monod's bacterial growth model revisited. Bltn Mathcal Biology 54, 117–122 (1992). https://doi.org/10.1007/BF02458623

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458623

Keywords

Search

Navigation